Haryana Police Constable Model Paper 1

Given:
The speed of two trains is 80 $\frac{\mathrm{km}}{\mathrm{hr}}$ and 90 $\frac{\mathrm{km}}{\mathrm{hr}}$
Concept used:
$\mathrm{Speed}=\frac{\mathrm{Distance}}{\mathrm{Time}}$
The relative speed in the same direction = Difference of speed
Calculation:
The relative speed of both train as they are moving in the same direction
⇒(90 – 80) $\frac{\mathrm{km}}{\mathrm{hr}}$ =10 $\frac{\mathrm{km}}{\mathrm{hr}}$
Relative speed in $\frac{\mathrm{m}}{\mathrm{s}}$
$\Rightarrow 10\times \frac{5}{18}=\frac{25}{9}\frac{\mathrm{m}}{\mathrm{s}}$
Now distance covered by the faster train is equal to its length (X).
Time taken = 54 secs
Distance = speed × time
$\Rightarrow \mathit{X}=\frac{25}{9}\times 54=150\mathrm{m}$
∴ The length of the faster train is 150 m.